As anybody who has studied Quantum Optics knows, correlation functions play a very large role in our understanding of the behavior of light. Roughly speaking, the correlation function tells you how likely you are to detect a second photon some short time after detecting one photon from some source. This shows up in the famous Hanbury Brown and Twiss experiment, and definitive proof of the existence of photons was provided in 1977 when Kimble, Dagenais and Mandel demonstrated photon anti-bunching, where the correlation function goes to zero for short times.

Correlation functions are a powerful technique for the study of physical systems. With that in mind, let us apply the technique to the problem of a hungry baby, SteelyKid for example. Here is a histogram of the intervals between feedings, as recorded over the three weeks since SteelyKid’s birth:

(Error bars represent 1-σ statistical uncertainties.)

We can immediately see from this graph that, as in the Kimble, Dagenais, and Mandel experiment, the probability of a second feeding occurring very shortly after the first is extremely low. This is unambiguous evidence of the quantization of baby-feeding– having eaten once, SteelyKid is unable to eat again until after a digestion period has passed. There is a peak in the distribution of feeding times suggesting an average digestion period of approximately 90 minutes.

The other striking feature of this figure is the appearance of a second peak in the time distribution, between 150 and 210 minutes. This is most likely an artifact caused by medical advice: in the first two weeks after SteelyKid’s birth, we were advised to feed her at least once every three hours (180 minutes), and to wake her up for feeding if necessary. This creates a large increase in the number of feedings right around 180 minutes, and a corresponding depletion in the longer-time tail of the distribution.

We can see this more clearly in the second figure, where we separate the data into feedings from the first two weeks, and feedings from the period after the pediatrician appointment where we were told to switch to feeding on demand:

The large excess peak due to waking her up to eat is clearly visible in the early data, but much less pronounced in the later period data. Interestingly, there is still a peak in the number of feedings between 180 and 210 minutes (at the 2.2-σ level). It is not clear whether this represents a residual effect of the earlier pattern, a statistical artifact, or the existence of a new feeding-time resonance that is not predicted in the Standard Model of Baby Feeding.

More data will be required to answer these questions. Additionally, we hope that the release of these results will spur renewed interest in ab initio calculations of feeding-time distributions, to compare with the data that we anticipate in the coming months, when the Large Infant Collider begins operation.

Perry: you must be getting more sleep that I got with my infant son, or you are truly a god among geeks to plot this!!!!

I don’t have the right plumbing to be able to help with the feeding, and it was something to do while SteelyKid was nursing.

Wilson: {Re: waking the baby for food} Because she wouldn’t be able to get hungry on her own? I’m interested in the reasoning behind this.

I’m not sure exactly. I think from what the nurses were saying that they’re worried that really small infants won’t necessarily wake up due to hunger, and then the lack of food makes them even sleepier, and they just waste away.

The change to “feed on demand” was made after she passed her birth weight (rocketed right past it, in fact), and we had established that she was eating well enough to gain weight. At that point, I guess they figure the kid’s got a grasp of the whole food thing, and can be trusted to handle it herself.

(The graph of SteelyKid’s mass over time only has four data points so far, which isn’t enough to fit a functional form. We don’t have a scale with the necessary precision, so that post will wait for a few more pediatrician visits…)

Referee Report: “Babies Are Quantized” is a provocative first draft. The inference may or may not be valid. A supportive experiment might be useful, although distasteful to the experimentalist, in which, instead of just measuring mass input as a function of time, also measuring mass output as a function of time. Conventional theory emphasizes gaseous output (mostly CO2 and water vapor), liquid output of salt solutions and trace organics from sweat glands and cache-dumping, and solid output from skin-flaking, hair-removal, fingernail/toenail clipping, and the nonlinear peristalsis mechanism (which is not fully understood, with some 35 different classes of mathematical models in the literature). I think that we may safely assume conservation of mass. It’s a cuious thing, as strange as the Id, that whatever SteelyKid eats (and does not excrete) turns into SteelyKid.

Since your distribution is changing over time, and the changes over time are at least as interesting as the frequency properties, you might consider doing some more sophisticated time-frequency analysis. You could try Leon Cohen’s introductory book, “Time-frequency analysis”, Prentice-Hall c1995, or his Proceedings of the IEEE 77, 941 (1989), “Time-Frequency Distributions-A Review”. Wikipedia is haphazard on this topic. Time-frequency analysis is something a Physicist should have in their toolset, as well as a baby for the experimentum crucis.

First of all, you are awesome. I gathered the same data (a year ago now!) and thought I would have time to plot it, but never did. At the time, I thought maybe I would see some sort of pattern that would help me know what the baby was planning to do next. I doubt it would’ve helped :)

“I don’t have the right plumbing to be able to help with the feeding, and it was something to do while SteelyKid was nursing.”

Actually, you are lacking only in hormones, your plumbing is probably fine for lactation, although our culture likely prevents you from wanting to take hormones and find out!

There is a peak in the distribution of feeding times suggesting an average digestion period of approximately 90 minutes.

There may be two peaks for weeks 1-2 and 2-3 in the Steelykid data set. For weeks 1-2, at ~75 and ~150 minutes; for weeks 2-3, at ~105 and ~210 minutes. I’m not familiar with infant circadian rhythms, but I know that adults have two circadian peaks for various physiological functions (heart rate, body temp, blood pressure, alertness, etc). Would be interesting to see if the feeding pattern correlates with heart rate, body temp, and sleep-wake cycle.

Relative to week 1-2, it looks like there’s been a forward phase shift of ~30 minutes for the first peak and ~60 minutes for the second, along with a general lengthening of the temporal frequency between the peaks (weeks 1-2: ~75 minutes; weeks 2-3: ~105 minutes) for weeks 2-3.

There’s also a noticeable decrease in Steelykid’s feeding amplitude relative to weeks 1-2.

It doesn’t appear that these patterns can be explained by fixed-interval (weeks 1-2) or fixed/variable ratio (weeks 2-3) reinforcement schedules, because the feeding amplitudes don’t quite match the predicted response patterns.

Books

You've read the blog, now try the books:

Eureka: Discovering Your Inner Scientist will be published in December 2014 by Basic Books. "This fun, diverse, and accessible look at how science works will convert even the biggest science phobe." --Publishers Weekly (starred review) "In writing that is welcoming but not overly bouncy, persuasive in a careful way but also enticing, Orzel reveals the “process of looking at the world, figuring out how things work, testing that knowledge, and sharing it with others.”...With an easy hand, Orzel ties together card games with communicating in the laboratory; playing sports and learning how to test and refine; the details of some hard science—Rutherford’s gold foil, Cavendish’s lamps and magnets—and entertaining stories that disclose the process that leads from observation to colorful narrative." --Kirkus ReviewsGoogle+

How to Teach Relativity to Your Dog is published by Basic Books. "“Unlike quantum physics, which remains bizarre even to experts, much of relativity makes sense. Thus, Einstein’s special relativity merely states that the laws of physics and the speed of light are identical for all observers in smooth motion. This sounds trivial but leads to weird if delightfully comprehensible phenomena, provided someone like Orzel delivers a clear explanation of why.” --Kirkus Reviews "Bravo to both man and dog." The New York Times.

How to Teach Physics to Your Dog is published by Scribner. "It's hard to imagine a better way for the mathematically and scientifically challenged, in particular, to grasp basic quantum physics." -- Booklist "Chad Orzel's How to Teach Physics to Your Dog is an absolutely delightful book on many axes: first, its subject matter, quantum physics, is arguably the most mind-bending scientific subject we have; second, the device of the book -- a quantum physicist, Orzel, explains quantum physics to Emmy, his cheeky German shepherd -- is a hoot, and has the singular advantage of making the mind-bending a little less traumatic when the going gets tough (quantum physics has a certain irreducible complexity that precludes an easy understanding of its implications); finally, third, it is extremely well-written, combining a scientist's rigor and accuracy with a natural raconteur's storytelling skill." -- BoingBoing